Pauli semigroups and unistochastic quantum channels

Abstract

We adopt the perspective of similarity equivalence, in gate set tomography called the gauge, to analyze various properties of quantum operations belonging to a semigroup, $\Phi =e^{\mathcal{L}t}$,and therefore given through the Lindblad operator. We first observe that the non unital part of the channel decouples from the time evolution. Focusing on unital operations we restrict our attention to the single-qubit case, showing that the semigroup embedded inside the tetrahedron of Pauli channels is bounded by the surface composed of product probability vectors and includes the identity map together with the maximally depolarizing channel. Consequently, every member of the Pauli semigroup is unitarily equivalent to a unistochastic map, describing a coupling with one-qubit environment initially in the maximally mixed state, determined by a unitary matrix of order four.

10 pages, 2 figures

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Cited by in corpus (12)

• Gate Set Tomography
• Quantum stochastic processes and quantum non-Markovian phenomena
• Phase covariant qubit dynamics and divisibility
• On the universal constraints for relaxation rates for quantum dynamical semigroup
• Convex combinations of CP-divisible Pauli channels that are not semigroups
• Entanglement-Free Parameter Estimation of Generalized Pauli Channels
• Log-Convex set of Lindblad semigroups acting on $N$-level system
• Geometry of generalized Pauli channels
• On the Floquet analysis of commutative periodic Lindbladians in finite dimension
• Quantum simulation of Pauli channels and dynamical maps: algorithm and implementation
• Geometry of symmetric and non-invertible Pauli channels
• Accessible maps in a group of classical or quantum channels